1 files changed, 9 insertions, 1 deletions
diff --git a/src/ModularArithmetic/Montgomery/ZBounded.v b/src/ModularArithmetic/Montgomery/ZBounded.v
index d01a48d89..2da20ddcf 100644
--- a/src/ModularArithmetic/Montgomery/ZBounded.v
+++ b/src/ModularArithmetic/Montgomery/ZBounded.v
@@ -78,7 +78,7 @@ Section montgomery.
       eauto 6 using reduce_via_partial_correct, reduce_via_partial_in_range, decode_small_valid.
     Qed.
 
-    Theorem reduce_via_partial_correct
+    Lemma reduce_via_partial_correct''
       : Z.equiv_modulo modulus
                        (decode_small (proj1_sig (reduce_via_partial v)))
                        (decode_large v * R')
@@ -88,5 +88,13 @@ Section montgomery.
       apply decode_small_valid in H'.
       destruct reduce_via_partial_correct'; split; eauto; omega.
     Qed.
+
+    Theorem reduce_via_partial_correct
+      : decode_small (proj1_sig (reduce_via_partial v)) = (decode_large v * R') mod modulus.
+    Proof.
+      rewrite <- (proj1 reduce_via_partial_correct'').
+      rewrite Z.mod_small by apply reduce_via_partial_correct''.
+      reflexivity.
+    Qed.
   End correctness.
 End montgomery.